Mid Ohio is less than an hour drive, bring a motorcycle and drag some knee at the many track days they have during construction season.
Decent XC mountain biking at Mohican, Alum Creek, Chestnut Ridge, etc. No downhill or anything comparable to out West though. We do have some badass indoor MTB options though at Ray's in Cleveland or the Mine down in KY.
Get a stand up jetski for Alum Creek like a Superjet, SXR, or if you've got money go with an aftermarket flatwater ski.
Paintballing at Splatterpark. Their rules suck, but I don't think there are any decent fields around anymore.